# Express in terms of sine and cosine Calculator

## Get detailed solutions to your math problems with our Express in terms of sine and cosine step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here!

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### Difficult Problems

1

Solved example of express in terms of sine and cosine

$\frac{1-\tan\left(x\right)}{1+\tan\left(x\right)}$
2

Rewrite $1-\tan\left(x\right)$ in terms of sine and cosine functions

$1-\tan\left(x\right)$
3

Applying the tangent identity: $\displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$

$1+\frac{-\sin\left(x\right)}{\cos\left(x\right)}$
4

Combine all terms into a single fraction with $\cos\left(x\right)$ as common denominator

$\frac{\cos\left(x\right)-\sin\left(x\right)}{\cos\left(x\right)}$
5

In the original expression, replace the $1-\tan\left(x\right)$ with $\frac{\cos\left(x\right)-\sin\left(x\right)}{\cos\left(x\right)}$

$\frac{\frac{\cos\left(x\right)-\sin\left(x\right)}{\cos\left(x\right)}}{1+\tan\left(x\right)}$
6

Divide fractions $\frac{\frac{\cos\left(x\right)-\sin\left(x\right)}{\cos\left(x\right)}}{1+\tan\left(x\right)}$ with Keep, Change, Flip: $\frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}$

$\frac{\cos\left(x\right)-\sin\left(x\right)}{\cos\left(x\right)\left(1+\tan\left(x\right)\right)}$
7

Multiply the single term $\cos\left(x\right)$ by each term of the polynomial $\left(1+\tan\left(x\right)\right)$

$\frac{\cos\left(x\right)-\sin\left(x\right)}{\cos\left(x\right)+\tan\left(x\right)\cos\left(x\right)}$

Applying the tangent identity: $\displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$

$\frac{\sin\left(x\right)}{\cos\left(x\right)}\cos\left(x\right)$

Multiplying the fraction by $\cos\left(x\right)$

$\frac{\sin\left(x\right)\cos\left(x\right)}{\cos\left(x\right)}$

Simplify the fraction $\frac{\sin\left(x\right)\cos\left(x\right)}{\cos\left(x\right)}$ by $\cos\left(x\right)$

$\sin\left(x\right)$
8

Applying the trigonometric identity: $\tan\left(\theta\right)\cdot\cos\left(\theta\right)=\sin\left(\theta\right)$

$\frac{\cos\left(x\right)-\sin\left(x\right)}{\cos\left(x\right)+\sin\left(x\right)}$

$\frac{\cos\left(x\right)-\sin\left(x\right)}{\cos\left(x\right)+\sin\left(x\right)}$